
\begin{tikzpicture}[scale=.35]
  \coordinate[label=left:$A$] (A) at (0,8);
  \coordinate[label=below:$B$] (B) at (-6,0);
  \coordinate[label=below:$C$] (C) at (3,0);
  \coordinate[label=above right:$D$] (D) at ($ (A)!(B)!(C) $);
  \coordinate[label=left:$E$] (E) at ($ (A)!(C)!(B) $);
  \path[name path=BD] (B) -- (D);
  \path[name path=CE] (C) -- (E);
  \coordinate (rtBDC) at ($ (B)!(D)!(C) $);
  \coordinate (rtBEC) at ($ (B)!(E)!(C) $);
  \path[name path=DF] (D) -- (rtBDC);
  \path[name path=EG] (E) -- (rtBEC);
  \path[name intersections={of=CE and DF}]
    coordinate[label=above:$F$] (F) at (intersection-1);
  \path[name intersections={of=BD and EG}]
    coordinate[label=above left:$G$] (G) at (intersection-1);
  \path[name path=AP] (A) -- ($ (B)!1.5!(A) $);
  \path[name path=AQ] (A) -- ($ (C)!2!(A) $);
  \path[name path=DP] (D) -- ($ (F)!5!(D) $);
  \path[name path=EQ] (E) -- ($ (G)!5!(E) $);
  \path[name intersections={of=AP and DP}]
    coordinate[label=above:$P$] (P) at (intersection-1);
  \path[name intersections={of=AQ and EQ}]
    coordinate[label=above:$Q$] (Q) at (intersection-1);
  \coordinate (sec) at ($ (B)!2!(C) $);
  \pic[mark angle={cyan}{2mm}{1}] {right angle=B--E--C};
  \pic[mark angle={cyan}{2mm}{1}] {right angle=B--D--C};
  \pic[mark angle={cyan}{2mm}{1}] {right angle=C--rtBEC--E};
  \pic[mark angle={cyan}{2mm}{1}] {right angle=D--rtBDC--B};
  \draw (A) -- (B) -- (C) -- cycle (B) -- (D) (C) -- (E)
    (D) -- (rtBDC) (E) -- (rtBEC) (A) -- (P) (P) -- (D)
    (A) -- (Q) (P) -- (Q) -- (E);
  \draw[blue] (B) -- (sec) -- (Q) (E) -- (sec) (G) -- (sec);
\end{tikzpicture}
